It has recently been shown that the structured surface of a perfect conductor can support surface-plasmon-like modes [Pendry et al., Science 305, 847 (2004)]. Such structures have a thickness of at least the order of the wavelength. Here, using microwave wavelength radiation incident beyond the critical angle of a wax prism, we quantify the surface-plasmon-like dispersion for a metamaterial surface with a thickness very much smaller than the incident wavelength.